Which of the following numbers is a factor of 156? ${7,8,9,10,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $156$ by each of our answer choices. $156 \div 7 = 22\text{ R }2$ $156 \div 8 = 19\text{ R }4$ $156 \div 9 = 17\text{ R }3$ $156 \div 10 = 15\text{ R }6$ $156 \div 13 = 12$ The only answer choice that divides into $156$ with no remainder is $13$ $ 12$ $13$ $156$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $156$ $156 = 2\times2\times3\times13 13 = 13$ Therefore the only factor of $156$ out of our choices is $13$. We can say that $156$ is divisible by $13$.